Question

A ball and a heavy wall are moving towards each other as shown in the figure. Assuming collision to be elastic, find the speed of the ball immediately after the collision.

• A. $4\text{m/s}$
• B. $5\text{m/s}$
• C. $6\text{m/s}$
• D. $2\text{m/s}$

Answer 1

The correct option is A $4\text{m/s}$

Let the speed of the ball is $v$ and of the heavy wall is $v_0$ after collision.

From conservation of linear momentum, before and after collision,

$m\left(2\right)+M(-1)=mv+M{v}_0\left[m\text{is mass of ball and}M\text{is mass of heavy wall}\right]$

$\Rightarrow v_0=\frac{2m-M-mv}{M}=\frac{2m}{M}-1-\frac{mv}{M}$

$\Rightarrow v_0=-1\text{m/s}[\because M\text{is very large}]$

$\Rightarrow$ Heavy wall continues to move with the same velocity.

The situations are shown in the below figure.



Now, coefficient of restitution,

$e=\frac{v_2-v_1}{u_1-u_2}=\frac{-1-(-v)}{2-(-1)}=1\left[\text{Elastic Collision}\right]$

$\therefore v=4\text{m/s}$

Hence, option $\left(A\right)$ is the correct answer.